National Curriculum Links

• Mathematics Programmes of Study: Year 4 (Number - Multiplication and Division)
• Pupils should be able to:
  • Recall multiplication and division facts for multiplication tables up to 12 × 12
  • Use place value, multiplication and division facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers
  • Recognise and use factor pairs and commutativity in mental calculations
  • Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000

Learning Objectives

By the end of this lesson, pupils will be able to:

• Multiply any given number by 10 and 100 mentally, using place value knowledge.
• Divide any given number by 10 and 100 mentally, understanding the effect on place value.
• Explain the mathematical reasoning behind multiplying and dividing by 10 and 100.

Success Criteria

• I can mentally multiply numbers by 10 and 100.
• I can mentally divide numbers by 10 and 100.
• I can explain how the digits move when multiplying or dividing by 10 and 100.
• I can justify my answers using place value knowledge and number patterns.

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Lesson Overview (30 Minutes)

1. Starter / Introduction (5 minutes)

Objective: Engage pupils with a visual and conceptual hook; activate prior knowledge of place value.

• Engagement: Show an image of a large arrow labelled “×10” and another labelled “÷10” placed over a grid of numbers.
• Demonstrate with place value charts: Write a number like 356 and ask pupils: “What do you think happens to the digits when we multiply by 10?”
• Provide the visual cue: digits move one place to the left when multiplying by 10, and one place right when dividing by 10.

Targeted Questions: (Using Bloom’s Taxonomy)

• Remembering: What is 10 times 4?
• Understanding: Can you explain why the digits shift to the left when we multiply by 10?
• Applying: What happens to the number 45 when you multiply it by 100? How is this different from multiplying by 10?
• Analysing: Look at these two numbers: 320 ÷ 10 and 320 ÷ 100. How do the results compare, and why?
• Evaluating: If we divide 500 by 10 and then multiply by 10, will it be the same number? Why or why not?
• Creating: Can you create a real-life problem involving multiplying or dividing by 100?

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2. Modelling (7 minutes)

Example for pupils to copy into books:

Operation	Step-by-step Explanation	Answer
243 × 10	Move each digit one place value to the left (243 → 2430)	2430
150 × 100	Move digits two places to the left (150 → 15000)	15000
520 ÷ 10	Move digits one place value to the right (520 → 52)	52
4300 ÷ 100	Digits shift two places to the right (4300 → 43)	43

• Use a place value chart to reinforce digit movement.
• Highlight when zeros are added or removed.
• Notice special cases, such as when dividing leads to decimals (e.g., 50 ÷ 10 = 5.0).

AfL Opportunities:

• After each modelling example, pause and ask: "Can you explain why the digits move this way?"
• Ask individual pupils to demonstrate a similar calculation aloud to assess understanding before moving to independent work.

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3. Guided Practice (8 minutes)

Task: A two-part worksheet/activity with gradual complexity

• Part 1: Simple whole numbers (e.g., 12 × 10, 200 ÷ 10, 35 × 100, 500 ÷ 100)
• Part 2: Mixed whole numbers and decimals (e.g., 4.5 × 10, 0.56 × 100, 750.2 ÷ 10, 39.6 ÷ 100)

Challenge extension:

• Write the missing calculation: “___ × 10 = 350” (prompt pupils to work backwards).
• Word problem: “A school bought 45 packs of pencils. Each pack contains 10 pencils. How many pencils are there in total?” (Connect to multiplication by 10.)

Targeted whole-class questioning:

• What do you notice about the digits when you multiplied by 100?
• How do you know when to add zeros or move the decimal point?
• Can someone explain how dividing by 10 is different from dividing by 100?
• Choose a problem and explain your thinking to the class.

AfL Points:

• Collect mini whiteboards during practice to check for misconceptions.
• Ask targeted pupils to explain their answers and strategies aloud.

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4. Addressing Misconceptions and Difficulties (5 minutes)

Common Misconceptions:

• Pupils confuse multiplication by 10 and 100, thinking the number gets “bigger” but not recognising how the digits move.
• Dividing leads pupils to remove zeros incorrectly or confuse place value shifts.
• Decimal point movement is unclear and can cause errors, especially with decimal numbers.

Teaching Strategies:

• Use place value charts extensively.
• Emphasise "digit movement" language rather than just "putting zeros."
• Reinforce the difference between whole numbers and decimals when shifting digits.
• Use visual aids (arrows, counters, place value grids).

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5. Independent or Paired Task (3 minutes)

• Pupils complete 5 problems on their own or discuss answers with a partner:
  • 76 × 10 = ?
  • 5.4 × 100 = ?
  • 900 ÷ 10 = ?
  • 1430 ÷ 100 = ?
  • Explain why multiplying 25 by 100 is different from multiplying by 10.

Request pupils to write one sentence explaining their reasoning for one question.

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6. Plenary (2 minutes)

Quick Quiz: verbally ask 3-4 questions requiring explanations, for example:

• What happens to the digits when multiplying by 10? Show me an example.
• If you divide 560 by 100, what is the answer? Why?
• Why is multiplying by 100 the same as multiplying by 10 twice?

Reflection:

• Ask pupils to say one thing they found easy and one thing they found tricky.
• Highlight the importance of place value understanding.

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Resources Needed

• Whiteboard and marker
• Place value charts (visual aids)
• Mini whiteboards for AFL checks
• Worksheet with progressive tasks

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WOW Teacher Tips

• Use real-life contexts such as money or measures (e.g., "£5 multiplied by 10 means 10 times the amount").
• Incorporate physical movement: pupils “move” their own bodies right or left to represent moving digits when multiplying/dividing by 10 or 100.
• Challenge pupils to create their own questions and swap with partners to solve.
• Use digital tools if available (interactive place value charts / animations).

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This lesson follows both the White Rose Maths Scheme approach to place value and mental calculation strategies and aligns with the National Curriculum for England (Year 4) ensuring age-appropriate progression and engagement.